A solid sphere of radius R… - JEE Main 2020 Physics PYQ

JEE Main 2020 — Physics Electromagnetism

2020mcqhard

A solid sphere of radius $R$ carries a charge $Q+q$ distributed uniformly over its volume. A very small point like piece of it of mass $m$ gets detached from the bottom of the sphere and falls down vertically under gravity. This piece carries charge $q$ . If it acquires a speed $\nu$ when it has fallen through a vertical height $y$ (see figure), then (assume the remaining portion to be spherical)

JEE Main 2020 Physics, Electrostatics — question figure

Official previous-year question

Held on 5 Sept 2020 · Verified 6 Jul 2026.

Options

A
${v}^{2}=y[\frac{qQ}{4\pi {\epsilon }_{0}{R}^{2}ym}+g]$
B
${v}^{2}=y[\frac{qQ}{4\pi {\epsilon }_{0}R(R+y)m}+g]$
C
${v}^{2}=2y[\frac{QqR}{4\pi {\epsilon }_{0}(R+y{)}^{3}m}+g]$
D
${v}^{2}=2y[\frac{qQ}{4\pi {\epsilon }_{0}R(R+y)m}+g]$

Did you get this right?

Solution

By using total energy conservation

$\Delta \mathrm{KE}+(\Delta \mathrm{PE}{)}_{\text{electo}} +(\Delta \mathrm{PE}{)}_{\text{gravitation}} =0$

$\frac{1}{2}m{V}^{2}+(k\frac{Qq}{R+y}-k\frac{Qq}{R})+(-mgy)=0$

$\frac{1}{2}m{V}^{2}=mgy+kQq(\frac{1}{R}-\frac{1}{R+y});{V}^{2}=2gy+\frac{2kQq}{m}\frac{y}{R(R+y)}$

${V}^{2}=2y[\frac{qQ}{4\pi {\epsilon }_{0}R(R+y)m}+g]$

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Options

${v}^{2}=y[\frac{qQ}{4\pi {\epsilon }_{0}{R}^{2}ym}+g]$

${v}^{2}=y[\frac{qQ}{4\pi {\epsilon }_{0}R(R+y)m}+g]$

${v}^{2}=2y[\frac{QqR}{4\pi {\epsilon }_{0}(R+y{)}^{3}m}+g]$

${v}^{2}=2y[\frac{qQ}{4\pi {\epsilon }_{0}R(R+y)m}+g]$

Solution

By using total energy conservation

$\Delta \mathrm{KE}+(\Delta \mathrm{PE}{)}_{\text{electo}} +(\Delta \mathrm{PE}{)}_{\text{gravitation}} =0$

$\frac{1}{2}m{V}^{2}+(k\frac{Qq}{R+y}-k\frac{Qq}{R})+(-mgy)=0$

$\frac{1}{2}m{V}^{2}=mgy+kQq(\frac{1}{R}-\frac{1}{R+y});{V}^{2}=2gy+\frac{2kQq}{m}\frac{y}{R(R+y)}$

${V}^{2}=2y[\frac{qQ}{4\pi {\epsilon }_{0}R(R+y)m}+g]$

Options

Did you get this right?

Solution

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Options

Did you get this right?

Solution

Your note

JEE Main Electromagnetism in other years

More JEE Main Electromagnetism questions

Other Physics topics for JEE Main

Mechanics

Modern Physics

Optics

Thermodynamics

Waves & Oscillations

Keep practicing Electromagnetism